Question

(b) let x be the length of the hypotenuse. use the triangle you drew and the pythagorean theorem to fill in the blanks.

(c) find x, the length of the hypotenuse. give an exact answer (not a decimal approximation).

(d) each unit on the map represents 0.2 kilometers in real life. use your answer from part (c) to find the distance between the teacups and the bumper cars in real life. round your answer to the nearest tenth.

Explanation:

Step1: Apply Pythagorean Theorem

Assume the two legs of the right - triangle are \(a = 6\) and \(b = 6\). According to the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\) (where \(c\) is the hypotenuse). So \(6^{2}+6^{2}=x^{2}\).

Step2: Calculate \(x\)

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Step3: Convert the map distance to real - life distance

Since each unit on the map represents \(0.2\) kilometers and \(x = 6\sqrt{2}\) units on the map. The real - life distance \(d=0.2\times6\sqrt{2}\).

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Answer:

(c) \(x = 6\sqrt{2}\)
(d) \(1.7\) kilometers